if $V=\iiint A dv$ Where $A$ and $V$ are vectors Then taking the divergence of both sides
$\nabla \cdot V$ = $\nabla \cdot \iiint A dv$=$\iiint \nabla \cdot A dv$
My mathematical knowledge doesn't exceeds calculus 3 and I found this result in a physics book.
Intuitively it's true but I'm asking for a rigorous proof of it.